CIRCLE'S AREA

Circle is one the most fascinating shapes in mathematics.It is defined as 'a collection of points equidistant from a fixed point' in Euclidean geometry.It has many wonderful properties .For example it is considered as the largest known polygon [while considering each point of it as a side] and hence it's interior angle sum is infinite.


We must appreciate the Greeks for their creativity of comparing the area of a triangle with the area of a circle.Let me explain this;
We know that triangles are the basic shape in geometry.So the Greeks used the shape for finding the area of a circle .
The method they used are as follow,

• For this, we can imagine circle as a collection of triangles; whose one vertex intersects with all others vertices's at the the centre of the circle.
  
• now, we can imagine that the two sides formed from the vertexes of the formed triangles coincides . 
  
• We know that,

Area of a triangle = 1/2 base * height

In this case the height is equal to the radius of the circle and the sum of  lengths of bases is equal to the circumference of the circle .From this,

Sum of bases of the triangles = Circumference of circle =2

π

r

 

Height of the triangle = Radius of the circle = rArea of a triangle= 1/2 base * height
So,

Area of the circle = Sum of areas of all triangles = 1/2 sum of all the bases  * height
=1/2 * circumference * radius

=1/2*2

πr*r=

π

r

2

It's amazing to know how creative the Greeks were .........WONDERFUL...

The below video finds the area of a circle using the area of a rectangle ..

LOVE MATHS + -/++